NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  syl3anl GIF version

Theorem syl3anl 1233
Description: A triple syllogism inference. (Contributed by NM, 24-Dec-2006.)
Hypotheses
Ref Expression
syl3anl.1 (φψ)
syl3anl.2 (χθ)
syl3anl.3 (τη)
syl3anl.4 (((ψ θ η) ζ) → σ)
Assertion
Ref Expression
syl3anl (((φ χ τ) ζ) → σ)

Proof of Theorem syl3anl
StepHypRef Expression
1 syl3anl.1 . . 3 (φψ)
2 syl3anl.2 . . 3 (χθ)
3 syl3anl.3 . . 3 (τη)
41, 2, 33anim123i 1137 . 2 ((φ χ τ) → (ψ θ η))
5 syl3anl.4 . 2 (((ψ θ η) ζ) → σ)
64, 5sylan 457 1 (((φ χ τ) ζ) → σ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358   w3a 934
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator